A propositional function is an expression containing a variable and becoming a proposition as soon as a value is assigned to the variable. For example, 'x is a man' is a propositional function. If, in place of x, we put Socrates or Plato or anybody else, we get a proposition. We can also replace x by something that is not a man and we still get a proposition, though in this case a false one. A propositional function is nothing but an expression. It does not, by itself, represent anything. But it can form part of a sentence which does say something, true or false:
Source: My Philosophical Development, chap. 6,1959
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